By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.

In recent years, various methods and benchmarks have been proposed to empirically evaluate the alignment of artificial neural networks to human neural and behavioral data. But how aligned are different alignment metrics? To answer this question, we analyze visual data from Brain-Score (Schrimpf et al., 2018), including metrics from the model-vs-human toolbox (Geirhos et al., 2021), together with human feature alignment (Linsley et al., 2018; Fel et al., 2022) and human similarity judgements (Muttenthaler et al., 2022). We find that pairwise correlations between neural scores and behavioral scores are quite low and sometimes even negative. For instance, the average correlation between those 80 models on Brain-Score that were fully evaluated on all 69 alignment metrics we considered is only 0.198. Assuming that all of the employed metrics are sound, this implies that alignment with human perception may best be thought of as a multidimensional concept, with different methods measuring fundamentally different aspects. Our results underline the importance of integrative benchmarking, but also raise questions about how to correctly combine and aggregate individual metrics. Aggregating by taking the arithmetic average, as done in Brain-Score, leads to the overall performance currently being dominated by behavior (95.25% explained variance) while the neural predictivity plays a less important role (only 33.33% explained variance). As a first step towards making sure that different alignment metrics all contribute fairly towards an integrative benchmark score, we therefore conclude by comparing three different aggregation options.

Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generate samples from complex distribution e.g. natural images. However, is there any universal structure in the gradient field that will eventually be learned by any neural network? Here, we aim to find such structures through a normative analysis of the score function. First, we derived the closed-form solution to the scored-based model with a Gaussian score. We claimed that for well-trained diffusion models, the learned score at a high noise scale is well approximated by the linear score of Gaussian. We demonstrated this through empirical validation of pre-trained images diffusion model and theoretical analysis of the score function. This finding enabled us to precisely predict the initial diffusion trajectory using the analytical solution and to accelerate image sampling by 15-30\% by skipping the initial phase without sacrificing image quality. Our finding of the linear structure in the score-based model has implications for better model design and data pre-processing.

There is a growing interest in using Generative Adversarial Networks (GANs) to produce image content that is indistinguishable from a real image as judged by a typical person. A number of GAN variants for this purpose have been proposed, however, evaluating GANs is inherently difficult because current methods of measuring the quality of the output do not always mirror what is actually perceived by a human. We propose a novel approach that deploys a brain-computer interface to generate a neural score that closely mirrors the behavioral ground truth measured from participants discerning real from synthetic images. In this paper, we first compare the three most widely used metrics in the literature for evaluating GANs in terms of visual quality compared to human judgments. Second, we propose and demonstrate a novel approach using neural signals and rapid serial visual presentation (RSVP) that directly measures a human perceptual response to facial production quality independent of a behavioral response measurement. Finally we show that our neural score is more consistent with human judgment compared to the conventional metrics we evaluated. We conclude that neural signals have potential application for high quality, rapid evaluation of GANs in the context of visual image synthesis.